Stable outcomes in cooperative games: There is an extensive literature of cooperative matching games dating back to the seminal work of [1]}. The major question is to existence of stable outcomes and efficient (polynomial order) algorithms for finding them. The games studied differ in various ways—in the structure of the matching market (e.g., two-sided vs one-sided, one-to-one vs one-to many vs many-to-many, etc.), and in the particular notion of stability employed (strong stability, core stability, Nash stability, individual stability, contractual individual stability, etc). [1]} studied two-sided games with two-sided preferences and established the existence of a core stable outcome via a deferred acceptance algorithm that runs in time \(O(n^2)\) . Two-sided matching games with one-sided preferences and with ownership is studied in [3]} where the top-trading cycle algorithm demonstrates the existence of a core stable outcome calculated in time \(O(n^2)\) . Finally, two-sided games without ownership are studied in [4]}, who studied a class of “random serial dictatorship” algorithms, and in [5]}, who proposed a “core from random endowment mechanism.” While the majority of this work involves two-sided matching, [6]} studied core stable outcomes in one-sided team formation problems in the context of roommate matching. This is a special case of hedonic games where agents form disjoint partitions and have preferences only in terms of agents in their own coalition [7]}. Hedonic games do not have core stable outcomes in general.
[7]} show that hedonic game with ordered coalitions or when players have additive and separable preferences have individually stable coalitions.
